Anomalies are a set of samples that do not follow the normal behavior of the majority of data. In an industrial dataset, anomalies appear in a very small number of samples. Currently, deep learning-based models have achieved important advances in image anomaly detection. However, with general models, real-world application data consisting of non-ideal images, also known as poison images, become a challenge. When the work environment is not conducive to consistently acquiring a good or ideal sample, an additional adaptive learning model is needed. In this work, we design a potential methodology to tackle poison or non-ideal images that commonly appear in industrial production lines by enhancing the existing training data. We propose Hierarchical Image Transformation and Multi-level Features (HIT-MiLF) modules for an anomaly detection network to adapt to perturbances from novelties in testing images. This approach provides a hierarchical process for image transformation during pre-processing and explores the most efficient layer of extracted features from a CNN backbone. The model generates new transformations of training samples that simulate the non-ideal condition and learn the normality in high-dimensional features before applying a Gaussian mixture model to detect the anomalies from new data that it has never seen before. Our experimental results show that hierarchical transformation and multi-level feature exploration improve the baseline performance on industrial metal datasets.
Recent studies have shown that independent identical distributed Gaussian
random variables is not suitable for modelling extreme values observed during extremal
events. However, many real life data on extreme values are dependent and stationary
rather than the conventional independent identically distributed data. We propose a stationary
autoregressive (AR) process with Gumbel distributed innovation and characterise
the short-term dependence among maxima of an (AR) process over a range of sample
sizes with varying degrees of dependence. We estimate the maximum likelihood of the
parameters of the Gumbel AR process and its residuals, and evaluate the performance
of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto
(GPD) distribution and we evaluate the performance of the parameter estimates fitted
to the cluster maxima and the original series. Ignoring the effect of dependence leads to
overestimation of the location parameter of the Gumbel-AR (1) process. The estimate
of the location parameter of the AR process using the residuals gives a better estimate.
Estimate of the scale parameter perform marginally better for the original series than the
residual estimate. The degree of clustering increases as dependence is enhance for the AR
process. The Gumbel-AR(1) fitted to the threshold exceedances shows that the estimates
of the scale and shape parameters fitted to the cluster maxima perform better as sample
size increases, however, ignoring the effect of dependence lead to an underestimation of
the parameter estimates of the scale parameter. The shape parameter of the original
series gives a superior estimate compare to the threshold excesses fitted to the Gumbel
distributed Generalised Pareto ditribution.
The well-known geostatistics method (variance-reduction method) is commonly used to determine the optimal rain gauge network. The main problem in geostatistics method to determine the best semivariogram model in order to be used in estimating the variance. An optimal choice of the semivariogram model is an important point for a good data evaluation process. Three different semivariogram models which are Spherical, Gaussian and Exponential are used and their performances are compared in this study. Cross validation technique is applied to compute the errors of the semivariograms. Rain-fall data for the period of 1975 – 2008 from the existing 84 rain gauge stations covering the state of Johor are used in this study. The result shows that the exponential model is the best semivariogram model and chosen to determine the optimal number and location of rain gauge station.
In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by an external force and alters the Gaussian structure of the system's fluctuations. In addition, by solving this extended equation, we provide a physical interpretation for the statistical properties of the fluctuations in these systems. Connections of the extended Langevin equation with the theory of active Brownian motion are discussed as well.
A multivariate control chart is a common tool used for monitoring and controlling a process whose quality is determined by several related variables. The objective of this study is to compare the performances of the multivariate exponentially weighted moving average (MEWMA) and the multivariate synthetic T2 control charts, for the case of a multivariate normally distributed process. A comparative study is made based on the average run length (ARL) performances of the control charts, using the simulation method, in order to identify the chart having the best performance in monitoring the process mean vector. The performances of the two charts, for different sample sizes and correlation coefficients, are presented in this paper. It was found that the MEWMA chart outperformed synthetic T2 chart for small shifts but the latter prevailed for moderate shifts. Both charts performed equally well for larger shifts. In addition, the performances of both MEWMA and synthetic T2 charts were found to be influenced by sample size and correlation coefficient. The two charts’ performances improved as the sample size and correlation coefficient increased for small and moderate shifts, but the charts’ performances did not depend on sample size and correlation coefficient when the shift was large.
Parameter estimation of complex exponential signals corrupted by additive white
Gaussian noise (AWGN) is crucial in the study of distributed beamforming in a practical
scenario. Near zero (0) phase offset are expected at the receiver end which rely on the
smoothing and correction of the frequency and phase estimates. Neither
computational complexity nor the processing latency has an effect on the expected
zero phase offset but the estimation accuracy does. Thus, the maximum likelihood
estimator (MLE) using Fast Fourier Transform (FFT) approach is being considered for
cases with none and post processing in locating of the maximum peaks. Details on how
the phase estimates are arrived at is not always covered in literatures but explained in
the article. Numerical results obtained showed that global maximum peaks are arrived
at by employing a fine search with higher values of FFT.
Hidden truncation (HT) and additive component (AC) are two well known paradigms of generating skewed distributions from known symmetric distribution. In case of normal distribution it has been known that both the above paradigms lead to Azzalini's (1985) skew normal distribution. While the HT directly gives the Azzalini's ( 1985) skew normal distribution, the one generated by AC also leads to the same distribution under a re parameterization proposed by Arnold and Gomez (2009). But no such re parameterization which leads to exactly the same distribution by these two paradigms has so far been suggested for the skewed distributions generated from symmetric logistic and Laplace distributions. In this article, an attempt has been made to investigate numerically as well as statistically the closeness of skew distributions generated by HT and AC methods under the same re parameterization of Arnold and Gomez (2009) in the case of logistic and Laplace distributions.
A gene regulatory network (GRN) is a large and complex network consisting of interacting elements that, over time, affect each other's state. The dynamics of complex gene regulatory processes are difficult to understand using intuitive approaches alone. To overcome this problem, we propose an algorithm for inferring the regulatory interactions from knock-out data using a Gaussian model combines with Pearson Correlation Coefficient (PCC). There are several problems relating to GRN construction that have been outlined in this paper. We demonstrated the ability of our proposed method to (1) predict the presence of regulatory interactions between genes, (2) their directionality and (3) their states (activation or suppression). The algorithm was applied to network sizes of 10 and 50 genes from DREAM3 datasets and network sizes of 10 from DREAM4 datasets. The predicted networks were evaluated based on AUROC and AUPR. We discovered that high false positive values were generated by our GRN prediction methods because the indirect regulations have been wrongly predicted as true relationships. We achieved satisfactory results as the majority of sub-networks achieved AUROC values above 0.5.
Image processing is introduced to remove or reduce the noise and unwanted signal that deteriorate the quality of an image. Here, a single level two-dimensional wavelet transform is applied to the image in order to obtain the wavelet transform sub-band signal of an image. An estimation technique to predict the noise variance in an image is proposed, which is then fed into a Wiener filter to filter away the noise from the sub-band of the image. The proposed filter is called adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in the wavelet domain. The performance of this filter is compared with four existing filters: median filter, Gaussian smoothing filter, two level wavelet transform with Wiener filter and adaptive noise Wiener filter. Based on the results, the adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in wavelet domain has better performance than the other four methods.
Kajian garis pangkal pengimejan resonans magnet kefungsian (fMRI) telah dijalankan ke atas 2 orang subjek lelaki sihat (kidal dan tidak kidal) masing-masing berumur 22 dan 25 tahun. Imbasan fMRI dijalankan menggunakan sistem pengimejan resonans magnet (MRI) 1.5 T di Jabatan Radiologi, Hospital Universiti Kebangsaan Malaysia. Kajian ini menggunakan gerakanjari tangan kanan dan kiri untuk merangsang aktiviti neuron di dalam korteks serebrum. Paradigma 5 kitar aktifIrehat digunakan dengan setiap kitar mengandungi satu blok aktif dan satu blok rehat yang masing-masing mengandungi 10 siri pengukuran. Imej fMRI dianalisis menggunakan pekej perisian MatLab dan pemetaan statistik berparameter 2 (sPM2). Proses pendaftaran jasad tegar menggunakan penjelmaan afin 6 parameter dilakukan ke atas kesemua imej kefungsian berwajaran T2*. Keputusan menunjukkan bahawa pergerakan subjek adalah minimum sama ada dalam arah translasi (< 1 mm) atau putaran (< 1 ). Kesemua imej dinormalkan melalui proses peledingan tak linear menggunakan penjelmaan afin 12 parameter dan didapati sepadan dengan pencontoh yang telahpun mematuhi ruang anatomi piawai. Walau bagaimanapun, bentuk, resolusi dan kontras imej kefungsian telah berubah sedikit berbanding dengan imej asal. Pelicinan imej menggunakan kernel Gaussian isotropik 6 mm menyebabkan data imej lebih bersifat parametrik dengan kehilangan yang ketara dalam resolusi dan kontras. Pengasingan struktur yang dilakukan ke atas imej berwajaran T1 mengklaskan tisu otak kepadajirim kelabu, jirim putih dan bendalir serebrospina. Pasca pemprosesan ruang bagi imej kefungsian dan struktur menjadikan data imej bersifat parametrik dengan taburan jenis Gaussian dan sedia untuk dianalisis menggunakan model linear am dan teori medan rawak Gaussian.
Expectation Maximization (EM) algorithm has experienced a significant increase in terms of usage in many fields of study. In this paper, the performance of the said algorithm in finding the Maximum Likelihood for the Gaussian Mixed Models (GMM), a probabilistic model normally used in fraud detection and recognizing a person’s voice in speech recognition field, is shown and discussed. At the end of the paper, some suggestions for future research works will also be given.
Setting a question paper for test, quiz, and examination is one of the teachers’ tasks. The factors that are usually taken into consideration in carrying out this particular task are the level of difficulty of the questions and the level of the students’ ability. In addition, teachers will also have to consider the number of questions that have impact on the examination. This research describes a model-based test theory to study the confidence intervals for the projected number of items of a test, given the reliability of the test, the difficulty of the question, and the students’ ability. Using the simulated data, the confidence intervals of the projected number of items were examined. The probability coverage and the length of the confidence interval were also used to evaluate the confidence intervals. The results showed that the data with a normal distribution, the ratio variance components of 4:1:5 and reliability equal to 0.80 gave the best confidence interval for the projected number of items.
Kajian pengimejan resonans magnet kefungsian (fMRI) subjek tunggal ini menyelidiki kesan daya dan laju tepikan ke atas sifat pengaktifan korteks berkaitan motor semasa tepikan jari rentak sendiri secara bilateral. Subjek melakukan empat cara tepikan jari rentak sendiri iaitu sentuh-perlahan (SP), sentuh-laju (SL), tekan-perlahan (TP) dan tekan-laju (TL) dalam satu imbasan fMRI. Model linear am (GLM) digunakan dalam penjanaan pengaktifan otak. Pentaakulan statistik kemudiannya dibuat mengenai pengaktifan otak menggunakan teori medan rawak (RFT) Gaussian pada aras keertian diperbetulkan (α = 0.05), dengan andaian tiada pengaktifan berlaku. Keputusan mendapati otak mengkoordinasi tepikan jari bilateral rentak sendiri dengan penglibatan korteks berkaitan motor iaitu girus presentral (PCG) bilateral, serebelum bilateral dan juga kawasan motor tambahan (SMA). Peningkatan daya tepikan menonjolkan pengaktifan yang bererti (p < 0.05 diperbetulkan) pada PCG bilateral (Kawasan Brodmann (BA) 6) sejajar dengan fungsinya dalam mencetus tindakan motor seperti mengawal daya tepikan. Peningkatan laju tepikan pula menyebabkan peningkatan pengaktifan otak secara bererti (p < 0.05 diperbetulkan) hanya pada korteks kesatuan somatoderia iaitu pada lobus parietal superior (SPL) kanan atau BA7 kanan. Ini mencadangkan bahawa SPL memainkan peranan penting dalam mengkoordinasi pergerakan berkemahiran terancang.
Computer vision is applied in many software and devices. The detection and
reconstruction of the human skeletal structure is one of area of interest, where the
camera will identify the human parts and construct the joints of the person standing in
front. Three-dimensional pose estimation is solved using various learning approaches,
such as Support Vector Machines and Gaussian processes. However, difficulties in
cluttered scenarios are encountered, and require additional input data, such as
silhouettes, or controlled camera settings. The paper focused on estimating the threedimensional
pose of a person without requiring background information, which is
robust to camera variations. Each of the joint has three-dimensional space position and
matrix orientation with respect to the sensor. Matlab Simulink was utilized to provide
communication tools with depth camera using Kinect device for skeletal detection.
Results on the skeletal detection using Kinect sensor is analysed in measuring the
abilities to detect skeletal structure accurately, and it is shown that the system is able
to detect human skeletal performing non-complex basic motions in daily life.
This paper deals with the analysis of different Fuzzy membership type performance for Extended Kalman Filter (EKF) based mobile robot navigation. EKF is known to be incompetent in non-Gaussian noise condition and therefore the technique alone is not sufficient to provide solution. Motivated by this shortcoming, a Fuzzy based EKF is proposed in this paper. Three membership types are considered which includes the triangular, trapezoidal and Gaussian membership types to determine the best estimation results for mobile robot and landmarks locations. Minimal rule design and configuration are also other aspects being considered for analysis purposes. The simulation results suggest that the Gaussian memberships surpassed other membership type in providing the best solution in mobile robot navigation.
In this paper, four types of circular probability distribution were used to evaluate which circular probability distribution gives the best fitting for southwesterly Malaysian wind direction data, namely circular uniform distribution, von Mises distribution, wrapped-normal distribution and wrapped-Cauchy distribution. The four locations chosen were Alor Setar, Langkawi, Melaka and Senai. Two performance indicators or goodness of fit tests which are mean circular distance and chord length were used to test which distribution give the best fitting.
In many statistical analyses, data need to be approximately normal or normally distributed. The Kolmogorov-Smirnov test, Anderson-Darling test, Cramer-von Mises test, and Shapiro-Wilk test are four statistical tests that are widely used for checking normality. One of the factors that influence these tests is the sample size. Given any test of normality mentioned, this study determined the sample sizes at which the tests would indicate that the data is not normal. The performance of the tests was evaluated under various spectrums of non-normal distributions and different sample sizes. The results showed that the Shapiro-Wilk test is the best normality test because this test rejects the null hypothesis of normality test at the smallest sample size compared to the other tests, for all levels of skewness and kurtosis of these distributions.
This paper analyzes the asymmetric long memory volatility dependency of the interday prices of Composite Index (CI) at Bursa Malaysia by using GARCH family models. The GARCH type models are used with the assumption that the innovations series follow either one of the following distributions: Gaussian, Student -t and skewed Student -t. The stock returns' long memory dependency is determined using the Hurst parameter. The long memory and asymmetric volatility are modelled by fractionally integrated GARCH models. It is found that the asymmetric and long memory GARCH models with skewed student-t distribution give better predictive ability on the volatility of the Kuala Lumpur Composite Index (KLCI).
This paper focuses on detecting outliers in the circular data which follow the wrapped normal distribution. We considered four discordance tests based on M, C, D and A statistics. The cut-off points of the four tests were obtained and the performance of the detection procedures was studied via simulations. In general, we showed that the discordance test based on the A statistic outperforms the other tests in all cases. For illustration, the city of Kuantan wind direction data set was considered.
The aim of researchers when comparing two independent groups is to collect large normally distributed samples unless they lack the resources to access them. In these situations, there are a myriad of non-parametric tests to select, of which the Mann Whitney U test is the most commonly used. In spite of its great advantages of usage, the U test is capable of producing inflated Type I error when applied in situation of heterogeneity or distinct variances. This current study will present a viable alternative called the refined Mann-Whitney test (RMW). A Monte Carlo evaluation test is conducted on RMW using artificial data of various combinations of extreme test conditions. This study reviews that the RMW test justified its development by enhancing the performance of the U test. The RMW test is able to control well its Type I error rates even though it has a lower power.